Well, it appears you have the script enabled and it can't be put into edit mode.

Which leaves, moving up one level and see if selecting the actual toolbox will enable you to edit it first.

If neither of those work, I would try this when the toolbox is added to arctoolbox rather than doing it from arccatalog.

And my final question, was whether it was a toolbox that was yours, or you got from somewhere else, that might be in a higher version, but encrypted. I know that you were using arccatalog 10.3, but the source/origin of the toolbox wasn't obvious.

Addendum

Click on Properties and report what is there as well. I am assuming that the script actually exists from the looks of it, but that is hidden.

Debugging

Custom toolboxes

Python toolboxes

IDEs can only debug Python files (.py). For Python code in script tool validation (embedded within a toolbox) the following approach can be used: copy the code to an external Python file and replace the code in the Python toolbox with the example below. You can then open the Python file in your IDE and set breakpoints, attach the IDE to ArcGIS Pro, and run your script tool. Upon completion of code modification, copy the contents of the Python file back into the tool validation.

IDEs can only debug Python files (.py). For code in a Python toolbox (.pyt file) the following approach can be used: copy the code to an external Python file, and replace the code in the Python toolbox with the example below. You can then open the Python file in your IDE and set breakpoints, attach the IDE to ArcGIS Pro, and use your Python toolbox. Upon completion of code modification, copy the contents of the Python file back into Python toolbox.

Which explains why you can't edit in Pro, so I presume that is the same case for your version of arcmap.

so it appears perhaps, that the process for Python toolboxes makes 'debug' and 'edit' a bit of an 'as designed' and your other bracketed comments